Paper 2026/1908 Original: eprint.iacr.org/2026/1908 ↗
A Generalized Wiener-type Attack Against a Family RSA-like Cryptosystems
Abstract
Let $N = pq$ be the product of two balanced prime numbers $p$ and $q$. In 2023, Cotan and Te\c seleanu introduced a family of RSA-like cryptosystems based on the key equation $ed - k(p^n - 1)(q^n - 1) = 1$, where $n \geq 1$. Note that when $n = 1$, we obtain the classical RSA scheme, while $n = 2$ yields the variant proposed by Elkamchouchi, Elshenawy, and Shaban. In this paper, we present a novel attack that combines continued fractions with lattice-based methods for the case $n = 2^i$, where $i > 2$ is an integer. This represents a natural continuation of previous research, which successfully applied similar techniques for $n = 1, 2, 4$.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2026-09-10: last updated
- 2026-09-07: published
- Short URL
- https://ia.cr/2026/1908
- License
- https://creativecommons.org/licenses/by-nc-sa/4.0/
BibTeX
@misc{cryptoeprint:2026/1908,
author = {George Teseleanu},
title = {A Generalized Wiener-type Attack Against a Family RSA-like Cryptosystems},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1908},
year = {2026},
url = {https://eprint.iacr.org/2026/1908}
}